Finite Group Databasebeta

← #49130251

Subgroups — #49130251

Order 36224.

372 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31826993C211yesmaximal, characteristic
2#31826595C211yesmaximal, characteristic, complemented
3#31826593C211yesmaximal, characteristic, complemented
4#31826538C211yesmaximal, characteristic, complemented
5#31826536C211yesmaximal, characteristic, complemented
6#31826534C211yesmaximal, characteristic, complemented
7#31826534C211yesmaximal, characteristic, complemented
8C8×D1132C211yesmaximal, characteristic, complemented
9C8×C22⋊D283C211yesmaximal, characteristic, complemented
10#31826526C211yesmaximal, characteristic, complemented
11#31826524C211yesmaximal, characteristic, complemented
12#31826516C211yesmaximal, characteristic, complemented
13#31826422C211yesmaximal, characteristic, complemented
14#97×D283C211yesmaximal, characteristic, complemented
15#405×C283C211yesmaximal, characteristic, complemented
16C2×#17985375C2211yescharacteristic
17C2×C8×D283C2211yescharacteristic
18C2×C8×D283C2211yescharacteristic
19C2×C8×D283C2211yescharacteristic
20#22583605C411yescharacteristic
21#22583603C411yescharacteristic
22#22583600C411yescharacteristic
23#22583596C411yescharacteristic
24#22583595C411yescharacteristic
25#22583592C411yescharacteristic
26#22583588C411yescharacteristic
27#22583583C411yescharacteristic
28C4×Dic566C2211yescharacteristic
29C4×D1132C2211yescharacteristic
30C4×C22⋊D283C2211yescharacteristic
31C4×C22⋊D283C2211yescharacteristic
32#22583567C2211yescharacteristic
33C42×D283C2211yescharacteristic
34C4⋊(C283⋊C8)C2211yescharacteristic
35C4⋊(C283⋊C8)C2211yescharacteristic
36Dic283⋊C8C2211yescharacteristic
37Dic283⋊C8C2211yescharacteristic
38Dic283⋊C8C2211yescharacteristic
39Dic283⋊C8C2211yescharacteristic
40C22⋊(C283⋊C8)C2211yescharacteristic
41C22⋊(C283⋊C8)C2211yescharacteristic
42(C2×D283)⋊C8C2211yescharacteristic
43(C2×D283)⋊C8C2211yescharacteristic
44(C2×D283)⋊C8C2211yescharacteristic
45(C2×D283)⋊C8C2211yescharacteristic
46#22583521C2211yescharacteristic
47#22583520C2211yescharacteristic
48#22583520C2211yescharacteristic
49#22583520C2211yescharacteristic
50C4×C283⋊C8C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52C2×M16×C283C2211yescharacteristic
53C22×C8×C283C2211yescharacteristic
54#117×C283C2211yescharacteristic
55#97×C283C2211yescharacteristic
56#97×C283C2211yescharacteristic
57C4×C8×C283C2211yescharacteristic
58C4×C8×C283C2211yescharacteristic
59C2×Dic566C2×C411yescharacteristic
60C2×D1132C2×C411yescharacteristic
61C2×C22⋊D283C2×C411yescharacteristic
62C2×C22⋊D283C2×C411yescharacteristic
63C2×C4×D283C2×C411yescharacteristic
64C2×C4×D283C2×C411yescharacteristic
65C2×C4×D283C2311yescharacteristic
66C2×C4×D283C2311yescharacteristic
67#17985375—22no—
68C2×C283⋊C8C2311yescharacteristic
69C2×C283⋊C8C2311yescharacteristic
70C2×C283⋊C8C2311yescharacteristic
71C2×C283⋊C8C2311yescharacteristic
72C8×D283—22no—
73C8×D283—22no—
74C8×D283—22no—
75C4⋊Dic283C2×C411yescharacteristic
76C4⋊Dic283C2×C411yescharacteristic
77Dic283⋊C4C2×C411yescharacteristic
78Dic283⋊C4C2×C411yescharacteristic
79Dic283⋊C4C2×C411yescharacteristic
80Dic283⋊C4C2×C411yescharacteristic
81Dic283⋊C4C2×C411yescharacteristic
82Dic283⋊C4C2×C411yescharacteristic
83C22⋊Dic283C2×C411yescharacteristic
84C22⋊Dic283C2×C411yescharacteristic
85(C2×D283)⋊C4C2×C411yescharacteristic
86(C2×D283)⋊C4C2×C411yescharacteristic
87(C2×D283)⋊C4C2×C411yescharacteristic
88(C2×D283)⋊C4C2×C411yescharacteristic
89(C2×D283)⋊C4C2×C411yescharacteristic
90(C2×D283)⋊C4C2×C411yescharacteristic
91C4×Dic283C2×C411yescharacteristic
92C4×Dic283C2×C411yescharacteristic
93C4×Dic283C2311yescharacteristic
94C4×Dic283C2311yescharacteristic
95C22×C4×C283C2311yescharacteristic
96M16×C283—22no—
97C2×C8×C283—22no—
98C2×C8×C283C2311yescharacteristic
99C2×C8×C283C2311yescharacteristic
100C2×C8×C283C2311yescharacteristic
101C2×C8×C283C2311yescharacteristic
102C4⋊C4×C283C2×C411yescharacteristic
103C4⋊C4×C283C2×C411yescharacteristic
104C22⋊C4×C283C2×C411yescharacteristic
105C22⋊C4×C283C2×C411yescharacteristic
106C42×C283C2311yescharacteristic
107C42×C283C2311yescharacteristic
108C22×D283C22×C411yescharacteristic
109C22×D283C22×C411yescharacteristic
110Dic566—41no—
111D1132—22no—
112C22⋊D283—22no—
113C22⋊D283—41no—
114C2×Dic283C22×C411yescharacteristic
115C2×Dic283C22×C411yescharacteristic
116C2×Dic283C22×C411yescharacteristic
117C2×Dic283C22×C411yescharacteristic
118C2×Dic283C22×C411yescharacteristic
119C2×Dic283C22×C411yescharacteristic
120C4×D283—22no—
121C4×D283—21no—
122C4×D283—21no—
123C4×D283—21no—
124C4×D283—21no—
125C4×D283—41no—
126C283⋊C8—21no—
127C283⋊C8—21no—
128C283⋊C8—21no—
129C283⋊C8—21no—
130C23×C283C22×C411yescharacteristic
131C2×C4×C283—21no—
132C2×C4×C283—21no—
133C2×C4×C283C22×C411yescharacteristic
134C2×C4×C283C22×C411yescharacteristic
135C2×C4×C283C22×C411yescharacteristic
136C2×C4×C283C22×C411yescharacteristic
137C2×C4×C283C22×C411yescharacteristic
138C2×C4×C283C2411yescharacteristic
139C8×C283—21no—
140C8×C283—21no—
141C8×C283#4112yes—
142C8×C283#4112yes—
143C22×C283—21no—
144C22×C283—21no—
145C22×C283—21no—
146C22×C283C23×C411yescharacteristic
147C2×D283—21no—
148C2×D283—21no—
149C2×D283—21no—
150C2×D283—21no—
151C2×D283—21no—
152C2×D283#13112yes—
153C4×C283—21no—
154C4×C283—21no—
155C4×C283—21no—
156C4×C283—21no—
157C4×C283—21no—
158C4×C283C2×#4111yescharacteristic
159C4×C283C2×#4111yescharacteristic
160Dic283—21no—
161Dic283—21no—
162Dic283—21no—
163Dic283—21no—
164Dic283—21no—
165Dic283—21no—
166C2×C283—41no—
167C2×C283C4×#4111yescharacteristic
168C2×C283C2×#13111yescharacteristic
169C2×C283#56811yescharacteristic
170D283—22no—
171D283—41no—
172C283#296811yescharacteristic, complemented, Sylow
173#2968—2831nomaximal, Sylow
174#529—2831no—
175#446—2831no—
176#446—2831no—
177#435—2831no—
178#435—2831no—
179#435—2831no—
180#435—2831no—
181C8×D4—2831no—
182C8×D4—2831no—
183#433—2831no—
184#433—2831no—
185#431—2831no—
186#405—2831no—
187#405D28311yescharacteristic, complemented
188C2×#97—2831no—
189C2×M16—2831no—
190C2×M16C2×D28311yescharacteristic
191C22×C8—2831no—
192C22×C8—2831no—
193C22×C8—2831no—
194C22×C8C2×D28311yescharacteristic
195#126—2831no—
196#126—2831no—
197#125—2831no—
198#124—2831no—
199#123—2831no—
200#123—2831no—
201C22⋊Q8—2831no—
202#121—2831no—
203C4×Q8—2831no—
204C4×D4—2831no—
205C4×D4—2831no—
206C4×D4—2831no—
207#117—2831no—
208#117C2×D28311yescharacteristic
209C2×C42—2831no—
210C4⋊C8—2831no—
211C4⋊C8—2831no—
212C4⋊C8—2831no—
213C4⋊C8—2831no—
214C4⋊C8—2831no—
215C4⋊C8—2831no—
216C22⋊C8—2831no—
217C22⋊C8—2831no—
218C22⋊C8—2831no—
219C22⋊C8—2831no—
220C22⋊C8—2831no—
221C22⋊C8—2831no—
222#97—2831no—
223#97—2831no—
224#97—2831no—
225#97—2831no—
226#97C2×D28311yescharacteristic
227#97C2×D28311yescharacteristic
228C4×C8—2831no—
229C4×C8—2831no—
230C4×C8C2×D28311yescharacteristic
231C4×C8C2×D28311yescharacteristic
232C2×Q8—2831no—
233C2×D4—2831no—
234C2×D4—2831no—
235C2×D4—2831no—
236C22×C4—2831no—
237C22×C4—2831no—
238C22×C4—2831no—
239C22×C4—2831no—
240C22×C4C22×D28311yescharacteristic
241M16—22no—
242M16—5662no—
243C2×C8—22no—
244C2×C8—2831no—
245C2×C8—2831no—
246C2×C8—2831no—
247C2×C8—2831no—
248C2×C8—5662no—
249C2×C8—5662no—
250C2×C8—5662no—
251C2×C8C22×D28311yescharacteristic
252C2×C8C22×D28311yescharacteristic
253C2×C8C22×D28311yescharacteristic
254C2×C8C22×D28311yescharacteristic
255C4⋊C4—2831no—
256C4⋊C4—2831no—
257C4⋊C4—2831no—
258C4⋊C4—2831no—
259C4⋊C4—2831no—
260C4⋊C4—2831no—
261C4⋊C4—2831no—
262C4⋊C4—2831no—
263C4⋊C4C4×D28311yescharacteristic
264C4⋊C4C4×D28311yescharacteristic
265C22⋊C4—2831no—
266C22⋊C4—2831no—
267C22⋊C4—2831no—
268C22⋊C4—2831no—
269C22⋊C4—2831no—
270C22⋊C4—2831no—
271C22⋊C4—2831no—
272C22⋊C4—2831no—
273C22⋊C4C4×D28311yescharacteristic
274C22⋊C4C4×D28311yescharacteristic
275C42—2831no—
276C42—2831no—
277C42—2831no—
278C42—2831no—
279C42C22×D28311yescharacteristic
280C42C22×D28311yescharacteristic
281C23—2831no—
282C23—2831no—
283C23C2×C4×D28311yescharacteristic
284Q8—11321no—
285D4—5662no—
286D4—5662no—
287D4—11321no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—2831no—
291C2×C4—2831no—
292C2×C4—2831no—
293C2×C4—2831no—
294C2×C4—2831no—
295C2×C4—2831no—
296C2×C4—5662no—
297C2×C4—5661no—
298C2×C4—5661no—
299C2×C4—5661no—
300C2×C4—5661no—
301C2×C4—11321no—
302C2×C4C2×C4×D28311yescharacteristic
303C2×C4C2×C4×D28311yescharacteristic
304C2×C4C2×C4×D28311yescharacteristic
305C2×C4C2×C4×D28311yescharacteristic
306C2×C4C2×C4×D28311yescharacteristic
307C2×C4C23×D28311yescharacteristic
308C8—21no—
309C8—21no—
310C8—5661no—
311C8—5661no—
312C8—5661no—
313C8—5661no—
314C8#1798539212yes—
315C8#1798539212yes—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—2832no—
320C22—5661no—
321C22—5661no—
322C22—5661no—
323C22—5661no—
324C22—5661no—
325C22C22×C4×D28311yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—5661no—
332C4—5661no—
333C4—5661no—
334C4—5661no—
335C4—5661no—
336C4—5661no—
337C4C2×#1798539211yescharacteristic
338C4C2×#1798539211yescharacteristic
339C2—41no—
340C2—5662no—
341C2—11321no—
342C2C4×#1798539211yescharacteristic
343C2#131×D28311yescharacteristic
344C2#3182723011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D283
commutator, socleC22×C283C23×C4
Fitting#405×C283C2
prime radical#22583583C4
cosocleC2×C4×C283C24
hypercenter#405D283
hypocenterC283#2968
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ #405

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #31826595C2semidirect
3. #31826593C2semidirect
4. #31826538C2semidirect
5. #31826536C2semidirect
6. #31826534C2semidirect
7. #31826534C2semidirect
8. C8×D1132C2semidirect
9. C8×C22⋊D283C2semidirect
10. #31826526C2semidirect
11. #31826524C2semidirect
12. #31826516C2semidirect
13. #31826422C2semidirect
14. #97×D283C2semidirect
15. #405×C283C2semidirect
172. C283#2968semidirect
187. #405D283semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#318269932
#318265952
#318265932
#318265382
#318265362
#318265342
C8×D11322
C8×C22⋊D2832
#318265262
#318265242
#318265162
#318264222
#97×D2832
#405×C2832
#2968283